Region distributions of graph embeddings and Stirling numbers

DOI10.1016/0012-365X(90)90045-JzbMath0706.05027OpenAlexW2041581800MaRDI QIDQ919004

Saul Stahl

Publication date: 1990

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0012-365x(90)90045-j

zbMATH Keywords

Stirling numbers of the first kindone-vertex, q-loop pseudo- graphorientable embeddingsregion distribution

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Enumeration in graph theory (05C30) Planar graphs; geometric and topological aspects of graph theory (05C10)

Related Items (22)

On the average genus of a graph ⋮ On the average crosscap number. II: Bounds for a graph ⋮ Bounds for the average genus of the vertex-amalgamation of graphs ⋮ Stratified graphs for imbedding systems ⋮ Permutation-partition pairs. III: Embedding distributions of linear families of graphs ⋮ Random 2-cell embeddings of multistars ⋮ Cubic graphs whose average number of regions is small ⋮ A tight lower bound on the maximum genus of a simplicial graph ⋮ Embedding distributions and Chebyshev polynomials ⋮ Total embedding distributions of Ringel ladders ⋮ An Introduction to Random Topological Graph Theory ⋮ On the genus distributions of wheels and of related graphs ⋮ Genus distribution of \(P_3 \mathop\square P_n\) ⋮ Genus distributions of star-ladders ⋮ Limit points for average genus. I: 3-connected and 2-connected simplicial graphs ⋮ On the number of maximum genus embeddings of almost all graphs ⋮ Limits for embedding distributions ⋮ Genera of Cayley maps ⋮ The average genus for bouquets of circles and dipoles ⋮ Total Embedding Distributions of Circular Ladders ⋮ Random Cayley maps for groups generated by involutions ⋮ Region distributions of some small diameter graphs

Cites Work

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• Factorization of permutations into n-cycles
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• Genus distributions for bouquets of circles
• Parallel concepts in graph theory
• Asymptotic Development of the Stirling Numbers of the First Kind
• Counting Cycles in Permutations by Group Characters, With an Application to a Topological Problem
• Permutation-Partition Pairs II: Bounds on the Genus of the Amalgamation of Graphs
• Theory of Maps on Orientable Surfaces
• Group Characters and the Structure of Groups
• On a Conjecture of Hammersley

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